https://file.aiquickdraw.com/mathbot/file/17285829670307h73emxl.jpg

Let's analyze the functions in the image and match them to their respective graph descriptions.

1. **\( g(x) = -3x^2 + 3x \)**:
   - This is a quadratic function (it has an \( x^2 \) term), meaning its graph is a parabola.
   - The coefficient of \( x^2 \) is negative (-3), so the parabola opens **downward**.
   - **Answer**: Parabola opening down.

2. **\( f(x) = 5 \)**:
   - This is a constant function, meaning no matter what \( x \) is, \( f(x) \) will always be 5.
   - The graph of a constant function is a **horizontal line**.
   - **Answer**: Horizontal line.

3. **\( h(x) = -3x - 3 \)**:
   - This is a linear function in the form \( y = mx + b \), where \( m = -3 \).
   - Since the slope is negative (-3), the graph is a **line with a negative slope**.
   - **Answer**: Line with a negative slope.

So, the correct answers are:
- (a) Parabola opening down
- (b) Horizontal line
- (c) Line with a negative slope

Would you like a detailed explanation of any of these functions?

Here are 5 related questions:
1. How do you determine the direction of a parabola from its equation?
2. What does the slope tell you about a line's orientation?
3. Can a quadratic equation ever represent a line?
4. Why is the graph of a constant function always a horizontal line?
5. How can you tell if a line has a positive or negative slope just by looking at its equation?

**Tip**: The sign of the leading coefficient in a quadratic equation determines whether the parabola opens up or down!

For each function below, choose the correct description of its graph.

Analyze different functions and match them to their correct graph descriptions. This problem covers quadratic functions, linear equations, and constant functions. Suitable for students in Grades 9-11.

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